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arXiv · 1809.03173

Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices

B. Senyange·B. Many Manda·Ch. Skokos
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Abstract

We numerically investigate the characteristics of chaos evolution during wave packet spreading in two typical one-dimensional nonlinear disordered lattices: the Klein-Gordon system and the discrete nonlinear Schrödinger equation model. Completing previous investigations \cite{SGF13} we verify that chaotic dynamics is slowing down both for the so-called `weak' and `strong chaos' dynamical regimes encountered in these systems, without showing any signs of a crossover to regular dynamics. The value of the finite-time maximum Lyapunov exponent $Λ$ decays in time $t$ as $Λ\propto t^{α_Λ}$, with $α_Λ$ being different from the $α_Λ=-1$ value observed in cases of regular motion. In particular, $α_Λ\approx -0.25$ (weak chaos) and $α_Λ\approx -0.3$ (strong chaos) for both models, indicating the dynamical differences of the two regimes and the generality of the underlying chaotic mechanisms. The spatiotemporal evolution of the deviation vector associated with $Λ$ reveals the meandering of chaotic seeds inside the wave packet, which is needed for obtaining the chaotization of the lattice's excited part.

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B. Senyange, B. Many Manda, Ch. Skokos. 2018-11-05. Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices. https://doi.org/10.1103/physreve.98.052229

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